Solve for $x$ and $y$ using elimination. $\begin{align*}-x-6y &= -3 \\ -7x-6y &= -3\end{align*}$
Answer: We can eliminate $y$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $-1$ and the bottom equation by $1$ $\begin{align*}x+6y &= 3\\ -7x-6y &= -3\end{align*}$ Add the top and bottom equations. $-6x = 0$ Divide both sides by $-6$ and reduce as necessary. $x = 0$ Substitute $0$ for $x$ in the top equation. $- 0-6y = -3$ $-6y = -3$ $-6y = -3$ $y = \dfrac{1}{2}$ The solution is $\enspace x = 0, \enspace y = \dfrac{1}{2}$.